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dc.contributor.authorBai, Ruobing
dc.contributor.authorWu, Yifei
dc.contributor.authorXue, Jun
dc.date.accessioned2021-03-05T15:20:08Z
dc.date.available2021-03-05T15:20:08Z
dc.date.created2020-09-29T14:19:10Z
dc.date.issued2020
dc.identifier.citationJournal of Differential Equations. 2020, 269 (9), 6422-6447.en_US
dc.identifier.issn0022-0396
dc.identifier.urihttps://hdl.handle.net/11250/2731961
dc.description.abstractIn this work, we consider the following generalized derivative nonlinear Schr\"odinger equation \begin{align*} i\partial_t u+\partial_{xx} u +i |u|^{2\sigma}\partial_x u=0, \quad (t,x)\in \R\times \R. \end{align*} We prove that when $\sigma\ge 2$, the solution is global and scattering when the initial data is small in $H^s(\R)$, $\frac 12\leq s\leq1$. Moreover, we show that when $0<\sigma<2$, there exist a class of solitary wave solutions $\{\phi_c\}$ satisfying $$ \|\phi_c\|_{H^1(\R)}\to 0, $$ when $c$ tends to some endpoint, which is against the small data scattering statement. Therefore, in this model, the exponent $\sigma\ge2$ is optimal for small data scattering. We remark that this exponent is larger than the short range exponent and the Strauss exponent.en_US
dc.language.isoengen_US
dc.publisherElsevieren_US
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internasjonal*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.no*
dc.titleOptimal small data scattering for the generalized derivative nonlinear Schrödinger equationsen_US
dc.typePeer revieweden_US
dc.typeJournal articleen_US
dc.description.versionacceptedVersionen_US
dc.source.pagenumber6422-6447en_US
dc.source.volume269en_US
dc.source.journalJournal of Differential Equationsen_US
dc.source.issue9en_US
dc.identifier.doihttps://doi.org/10.1016/j.jde.2020.05.001
dc.identifier.cristin1834976
dc.relation.projectNorges forskningsråd: 250070en_US
dc.description.localcode© 2020. This is the authors’ accepted and refereed manuscript to the article. Locked until 7/6-2022 due to copyright restrictions. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/en_US
cristin.ispublishedtrue
cristin.fulltextpostprint
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